Rodon was forced to exit his Minor League appearance early after being struck by a comebacker in the third inning of a rehab start at Triple-A Charlotte.
The 25-year-old lefty suffered a head laceration that required several staples, but he remains on track to make his next scheduled start for Charlotte, Renteria said.
"I couldn't tell you what he was going through at that moment, but the fact that he still wanted to remain in [the game] just shows you how he is," Renteria said. "He's a very strong competitor."
Rodon, who continues to work back from offseason shoulder surgery, fell to the ground but bounced up quickly before removing his hat and checking his forehead for blood.
He was met at the mound by a team trainer before being led back to the dugout.
"Obviously, it wouldn't have been the most prudent thing to [stay in the game] once you've been hit with a line drive," Renteria said. "You've got to make sure you check out, and make sure you're responding appropriately. But he was fine."
Prior to his exit, Rodon struck out six and allowed one hit in 2 2/3 scoreless innings against Triple-A Norfolk. He threw 40 pitches, including 29 for strikes.
"Carlos, once he gets out, he wants to continue to compete," Renteria said. "Fortunately for us, it wasn't anything more than that."
The ball, hit by Norfolk's D'Arby Myers, caromed off Rodon's head and into shallow left field, where Charlotte third baseman Jake Elmore made an impressive over-the-shoulder catch.
It was Rodon's second rehab outing, and first at Triple-A. He allowed one run on three hits in five innings pitched in his first rehab start with Class A Kannapolis last week.
"He's throwing very well. He feels very good, and he has command of the zone," Renteria said. "Everybody says he looks as relaxed as they've ever seen him. So that's good for us."
Other injuries Matt Davidson can't quite seem to shake those back spasms.
Davidson was held out of Chicago's lineup for a third consecutive game due to lingering back stiffness. He remains day to day, Renteria said Friday.
"He's doing better, and we'll continue to see how he goes through the rest of his day as they're treating him," Renteria added. "Back spasms are tricky. You don't want to create or cause them to happen again. But he's starting to feel better again."
Renteria said Davidson, who has been receiving treatment since being scratched from Wednesday's lineup, is eager to get back. He's batting .243 with 11 homers through 42 games.
"Thankfully, we have a group of men that want to keep pushing, and we do have to stop them. That's actually a good thing. Not necessarily a bad thing," Renteria said. "But we have to be mindful of where they're at, and what they're doing, and make sure that we take care of them."
James Schmehl is a contributor to MLB.com based in Detroit.